from __future__ import annotations

import time
from collections.abc import Sequence
from random import randint

from matplotlib import pyplot as plt


def 				lowerCAmelCase__       (			a__    ,     a__    ,     a__ )      ->tuple[int | None, int | None, float]:




  '''simple docstring'''

  if not arr:
    return None, None, 0
  if low == high:
    return low, high, arr[low]

  _UpperCamelCase           =    (low + high) // 2
  _UpperCamelCase      ,						_UpperCamelCase      ,						_UpperCamelCase           =    max_subarray(a__    ,     a__    ,     a__ )
  _UpperCamelCase      ,						_UpperCamelCase      ,						_UpperCamelCase           =    max_subarray(a__    ,     mid + 1    ,     a__ )
  _UpperCamelCase      ,						_UpperCamelCase      ,						_UpperCamelCase           =    max_cross_sum(a__    ,     a__    ,     a__    ,     a__ )
  if left_sum >= right_sum and left_sum >= cross_sum:
    return left_low, left_high, left_sum
  elif right_sum >= left_sum and right_sum >= cross_sum:
    return right_low, right_high, right_sum
  return cross_left, cross_right, cross_sum


def 				lowerCAmelCase__       (			a__    ,     a__    ,     a__    ,     a__ )      ->tuple[int, int, float]:




  '''simple docstring'''

  _UpperCamelCase      ,						_UpperCamelCase           =    float("-inf" ), -1
  _UpperCamelCase      ,						_UpperCamelCase           =    float("-inf" ), -1

  _UpperCamelCase           =    0
  for i in range(a__    ,     low - 1    ,     -1 ):
    summ += arr[i]
    if summ > left_sum:
      _UpperCamelCase           =    summ
      _UpperCamelCase           =    i

  _UpperCamelCase           =    0
  for i in range(mid + 1    ,     high + 1 ):
    summ += arr[i]
    if summ > right_sum:
      _UpperCamelCase           =    summ
      _UpperCamelCase           =    i

  return max_left, max_right, (left_sum + right_sum)


def 				lowerCAmelCase__       (			a__ )      ->float:




  '''simple docstring'''

  _UpperCamelCase           =    [randint(1    ,     a__ ) for _ in range(a__ )]
  _UpperCamelCase           =    time.time()
  max_subarray(a__    ,     0    ,     input_size - 1 )
  _UpperCamelCase           =    time.time()
  return end - start


def 				lowerCAmelCase__       (			)      ->None:




  '''simple docstring'''

  _UpperCamelCase           =    [10, 100, 1_000, 10_000, 50_000, 100_000, 200_000, 300_000, 400_000, 500_000]
  _UpperCamelCase           =    [time_max_subarray(a__ ) for input_size in input_sizes]
  print("No of Inputs\t\tTime Taken" )
  for input_size, runtime in zip(a__    ,     a__ ):
    print(a__    ,     "\t\t"    ,     a__ )
  plt.plot(a__    ,     a__ )
  plt.xlabel("Number of Inputs" )
  plt.ylabel("Time taken in seconds" )
  plt.show()


if __name__ == "__main__":
   from doctest import testmod

   testmod()





from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


lowerCamelCase__  =					{
    '''configuration_longformer''': [
        '''LONGFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''LongformerConfig''',
        '''LongformerOnnxConfig''',
    ],
    '''tokenization_longformer''': ['''LongformerTokenizer'''],
}

try:
   if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   lowerCamelCase__  =					['''LongformerTokenizerFast''']

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   lowerCamelCase__  =					[
       '''LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST''',
       '''LongformerForMaskedLM''',
       '''LongformerForMultipleChoice''',
       '''LongformerForQuestionAnswering''',
       '''LongformerForSequenceClassification''',
       '''LongformerForTokenClassification''',
       '''LongformerModel''',
       '''LongformerPreTrainedModel''',
       '''LongformerSelfAttention''',
   ]

try:
   if not is_tf_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   lowerCamelCase__  =					[
       '''TF_LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST''',
       '''TFLongformerForMaskedLM''',
       '''TFLongformerForMultipleChoice''',
       '''TFLongformerForQuestionAnswering''',
       '''TFLongformerForSequenceClassification''',
       '''TFLongformerForTokenClassification''',
       '''TFLongformerModel''',
       '''TFLongformerPreTrainedModel''',
       '''TFLongformerSelfAttention''',
   ]


if TYPE_CHECKING:
   from .configuration_longformer import (
       LONGFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
       LongformerConfig,
       LongformerOnnxConfig,
   )
   from .tokenization_longformer import LongformerTokenizer

   try:
      if not is_tokenizers_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_longformer_fast import LongformerTokenizerFast

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_longformer import (
          LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
          LongformerForMaskedLM,
          LongformerForMultipleChoice,
          LongformerForQuestionAnswering,
          LongformerForSequenceClassification,
          LongformerForTokenClassification,
          LongformerModel,
          LongformerPreTrainedModel,
          LongformerSelfAttention,
      )

   try:
      if not is_tf_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_tf_longformer import (
          TF_LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
          TFLongformerForMaskedLM,
          TFLongformerForMultipleChoice,
          TFLongformerForQuestionAnswering,
          TFLongformerForSequenceClassification,
          TFLongformerForTokenClassification,
          TFLongformerModel,
          TFLongformerPreTrainedModel,
          TFLongformerSelfAttention,
      )

else:
   import sys

   lowerCamelCase__  =					_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)




